How would an object need to move in order for total distance traveled and displacement to be equal?
1 answer:
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Answer:
The distance moved by the block is 1.34 m
Explanation:
Given;
initial velocity of the block, u = 3 m/s
angle of inclination, θ = 20⁰
The net horizontal force acting on the block;
∑Fx = - mgsinθ
Apply Newton's second law of motion, to determine the constant acceleration of the block.
∑Fx = ma
- mgsinθ = ma
-gsinθ = a
Apply the following Kinematic equation, to determine how far up, the block moved before coming to rest.
Therefore, the distance moved by the block is 1.34 m
If all you need is the initial speed of the cork, you can solve this using only two of your given:
2.00 m.s upward and 6.60 m.s horizontally.
If you take in consideration the movement of the cork, you know that it was both going up and forward at the same time, this means that it was moving at a diagonal direction. Now you can solve this by using the Pythagorean theorem where:
Why? Because the vertical and the horizontal motion creates a movement that is diagonal, which when put in a free-body diagram, creates a right triangle.
Going back to your problem, when applying this, the diagonal of a right triangle is the hypotenuse, so this is what you are looking for. The horizontal and vertical motion will represent the other 2 sides of the triangle.
Now let's put that into your formula:
Where: Vx is your horizontal velocity
Vy is your vertical velocity
Vi is your initial velocity
Now let's put in your given:
So your initial velocity is 6.8964 m/s or 6.90 m/s
2.00 m.s upward and 6.60 m.s horizontally.
If you take in consideration the movement of the cork, you know that it was both going up and forward at the same time, this means that it was moving at a diagonal direction. Now you can solve this by using the Pythagorean theorem where:
Why? Because the vertical and the horizontal motion creates a movement that is diagonal, which when put in a free-body diagram, creates a right triangle.
Going back to your problem, when applying this, the diagonal of a right triangle is the hypotenuse, so this is what you are looking for. The horizontal and vertical motion will represent the other 2 sides of the triangle.
Now let's put that into your formula:
Where: Vx is your horizontal velocity
Vy is your vertical velocity
Vi is your initial velocity
Now let's put in your given:
So your initial velocity is 6.8964 m/s or 6.90 m/s